The present invention relates to processes for demodulating frequency-modulated signals, demodulators using these processes and in particular SECAM television systems comprising such demodulators.
In the SECAM system, the color information modulates in frequency a subcarrier situated proximate the end of the highest frequencies and inside the luminance spectrum. This latter extends from 0 to about 6 MHz and the subcarrier, whose frequency deviation extends between 3.9 and 4.7 MHz is mixed with the principal spectrum. Different systems have been thought up for demodulating this subcarrier by means of conventional frequency discriminators which present the drawback of being sensitive to the amplitude variations of the signal to be processed.
There is described in U.S. patent application Ser. No. 205,503 a process for effecting digital demodulation of a frequency-modulated signal, more especially of a chrominance signal of a SECAM video signal, while presenting the advantage of not being sensitive to the amplitude variations of the low-frequency signal with respect to the central frequency.
This demodulation process consists, while considering the signal to be demodulated as being the projection on an axis Ox of a vector Z(t) rotating about a point 0 in an Oxy reference frame, in determining the variations of the frequency of the signal to be demodulated with respect to the variations of the rotational speed of the rotating vector, this determination being effected from the calculation of a linear combination ratio of samples of the value of the projection on the axis Ox of the rotating vector. In particular, one of the examples of the process described in U.S. patent application Ser. No. 205,503 consists in sampling the chrominance signal of a SECAM video signal at a rate equal to 4 times the central frequency F of the frequency band of the signal, then in determining the position of the rotating vector by means of two successive samples of the signal, and in determining a first value of the frequency variation between two times separated by (1/F) by comparing the position of the rotating vector at these times. The following formulae are established: ##EQU1## .delta.F being the value of the frequency deviation, .theta.(t) being the angle of the vector Z(t) with the axis Ox of the Oxy reference frame; this angle allows the position of the vector Z(t) to be located,
x(t) being the projection of the vector Z(t) on the axis Ox; x(t) corresponds therefore to the signal to be demodulated, PA1 y(t) being the projection on the axis Ox of the "in quadrature" vector with respect to Z(t); y(t) corresponds then to the projection on the axis Oy of the vector Z(t), PA1 .theta.(t) being an estimation of the angle .theta.(t), PA1 .DELTA..theta.(t') being an estimation of the angular variation between two positions of the vector Z(t) at times spaced apart by 1/F and .DELTA.F being the value of the frequency variation between two times spaced apart by (1/F).
Since the relative band of the chrominance signal is small with respect to the central frequency F=4.3 MHz, it has been considered in the calculation of the formulae 1, 2 and 3 that the value .delta.F/F is very much less than 1.
The error committed with respect to .DELTA.F due to this approximation (.delta.F/F)&lt;&lt;1 depends on the position of the vector and on the frequency to be demodulated.
In fact, according to formula 1: ##EQU2##
It may be shown that the error committed with respect to the angle .theta.(t) by application of the formula 10 is of the form: ##EQU3##
The first term (.epsilon..sup.2 /4) sin 2.theta.(t) due to the presence of the factor ##EQU4## in the expression of .theta.(t) (formula 10 is negligible with respect to the term ##EQU5## due to the presence of the term ##EQU6##
It may furthermore be demonstrated that the resulting error committed with respect to .DELTA.F after a calculation of the form ##EQU7## (formulae 2 and 3 is a function of the angle .theta.(t) by a term of the form sin 2.theta.(t). The error changes sign therefore for angles in quadrature. This is why there is envisaged in U.S. patent application Ser. No. 205,503 a first method for minimizing the error consisting in taking the arithmetic average of two values of .DELTA.F obtained from two positions approximately in quadrature of the vector Z(t).
The relative error ##EQU8## of the improved value .sup.2 .DELTA.F which results therefrom is modulated in amplitude by a sinusoidal function of the angle of the vector from which was calculated .DELTA.F about the value .epsilon..sup.2. Thus, the relative error ##EQU9## is of the order of .epsilon..sup.2 with ##EQU10##
As a complement to the first method of error minimization, there was also envisaged in U.S. patent application Ser. No. 205,503 a second method for improving the value .sup.2 .DELTA.F. This additional method of error minimization consists in calculating the value of a correction factor .epsilon..sub.n as a function of .DELTA.F and .theta.(t) and in deducing therefrom a final value .sup.3 .DELTA.F=(1-.epsilon..sub.n).sup.2 .DELTA.F of the frequency variation.
The process of the present invention has the advantage of replacing the average effected, according to the first error minimization method, on the approximate values .DELTA.F of the frequency deviation after arc tangent calculation (formula 1 ), by an average effected with the arc tangent calculation directly on the values of the samples of the signal to be demodulated. This allows the time available for calculating the values .theta.(t) to be multiplied by four, and so to make the practical execution of the system much easier.
The frequency for obtaining the calculated values .DELTA.F will then be F=4.3 MHz, of which the value is still considerably greater than the theoretical limit imposed by Shannon's theorem, considering the passband of the SECAM chrominance signals.
Futher, the relative error of the frequency deviation obtained by the process of the present invention is four times less than that of the frequency deviation .sup.2 .DELTA.F obtained by the process described in U.S. patent application Ser. No. 205,503.